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Chapter 28: Problem 39

List the number of electron states in each of the subshells in the \(n=7\) shell. What is the total number of electron states in this shell?

Short Answer

Expert verified
Answer: There are a total of 98 electron states in the n=7 shell. The number of electron states in each subshell is as follows: l=0: 2 electron states l=1: 6 electron states l=2: 10 electron states l=3: 14 electron states l=4: 18 electron states l=5: 22 electron states l=6: 26 electron states

Step by step solution

01

Identify the subshells for n=7

For n=7, there will be 7 subshells, each corresponding to a unique value of the azimuthal quantum number, l. The subshells will have l values ranging from 0 to 6 (l=0,1,2,3,4,5,6).
02

Calculate the number of electron states in each subshell

For each subshell, the electron states are determined by the magnetic quantum number, m. The possible values of m range from -l to l. We can calculate the number of electron states by using the formula 2 * (2l + 1) for each subshell. l=0: 2 * (2(0)+1) = 2 l=1: 2 * (2(1)+1) = 6 l=2: 2 * (2(2)+1) = 10 l=3: 2 * (2(3)+1) = 14 l=4: 2 * (2(4)+1) = 18 l=5: 2 * (2(5)+1) = 22 l=6: 2 * (2(6)+1) = 26
03

Calculate the total number of electron states for n=7

To find the total number of electron states in the n=7 shell, we add up the number of electron states in each subshell: 2+6+10+14+18+22+26 = 98 Thus, there are a total of 98 electron states in the n=7 shell.

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